Kun Fang

Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the phenomenon of superadditivity. This work develops Riemannian optimization methods to establish significantly tighter, computable two-sided bounds on these fundamental quantities. For upper bounds, our method systematically searches for state and channel extensions that minimize known information-theoretic bounds. We achieve this by parameterizing the space of all possible extensions as a Stiefel manifold, enabling a universal search that overcomes the limitations of ad-hoc constructions. Combined with an improved upper bound on the one-way distillable entanglement based on a refined continuity bound on quantum conditional entropy, our approach yields new state-of-the-art upper bounds on the quantum capacity of the qubit depolarizing channel for large values of the depolarizing parameter, strictly improving the previously best-known bounds. For lower bounds, we introduce Riemannian optimization methods to compute multi-shot coherent information. We establish lower bounds on the one-way distillable entanglement by parameterizing quantum instruments on the unitary manifold, and on the quantum capacity by parameterizing code states with a product of unitary manifolds. Numerical results for noisy entangled states and different channels demonstrate that our methods successfully unlock superadditive gains, improving previous results. Together, these findings establish Riemannian optimization as a principled and powerful tool for navigating the complex landscape of quantum communication limits. Furthermore, we prove that amortization does not enhance the channel coherent information, thereby closing a potential avenue for improving capacity lower bounds in general. This result can be of independent interest.

We study communication and discrimination over quantum channels with entanglement-enabled jammers. Using a minimax framework, we show universality reduces to worst-case optimization, yielding streamlined, dimension-independent characterizations of entanglement-assisted capacities and Stein-type error exponents for channel discrimination against quantum adversaries.

Abstract The manipulation of quantum resources such as entanglement and coherence lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to purify the quantum resources, since they are inevitably contaminated by noises and thus often lost their power or become unreliable for direct usage. In these two works, we establish a theory of the universal limitations on the accuracy and efficiency of resource purification tasks which apply to any well-behaved resource theory, for both state (static) and channel (dynamical) resources. The general results bring new insights and imply various forms of fundamental limits to a broad range of problems of great theoretical and practical importance, including magic state distillation and fault tolerant quantum computing, quantum error correction, quantum Shannon theory, and quantum circuit synthesis.

The pursuit of tight finite-key analysis for general QKD protocols is an exciting but challenging task for theorists. Entropy accumulation theorem (EAT) was developed recently and been successfully applied to device-independent QKD protocols. In the present work, we use EAT to prove the security of a very large class of entanglement-based QKD protocols, covering most discrete-variable protocols as well as their optical implementations.

In this work, we present an open-source software platform that calculates key rate for general QKD protocols, building upon the numerical framework proposed by our group that can perform automated security proof of QKD protocols. The software platform is fully modularized with mutually independent modules for descriptions of protocols/channels, solvers for bounding key rate, and parameter optimization algorithms. It currently supports BB84 and measurement-device-independent QKD (including decoy states), as well as discrete-modulated continuous variable QKD. It also supports finite-size analysis for non-decoy-state protocols. We hope that the open-sourcing can attract theorists to test new protocols and/or contribute to new solvers, as well as appeal to experimentalists who wish to analyze their data or optimize parameters for new experiments.

Randomness is one of the key ingredients to information processing in practice, especially for computation and cryptography. A vast number of applications critically rely on abundant, high-quality random numbers that are generated securely. In this work we introduce a variant of randomness extraction framework, named \emph{incoherent randomness extraction} (IRE), in the context of quantum coherence theory where free incoherent operations are employed. This cryptographic framework unveils a new perspective to the study of quantum coherence distillation (QCD) by an \emph{exact} one-shot connection, that is, the maximum number of secure random bits extractable from a single instance of \emph{unstructured} quantum state is precisely equal to the maximum number of coherent bits that can be distilled from the same state. This exact relation not only sharpens our understanding on the operational equivalence between randomness and coherence, but also enables us to derive tight second order expansions (estimation of the number of extractable random bits/distillable coherent bits to the order~$o(\sqrt{n})$ where $n$ is the number of the prepared source states) of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all lead to the same second order expansions, indicating their operational equivalence for QCD as well as IRE in both asymptotic and large block length regimes. As a by-product, we showcase a proof of the strong converse property for IRE from its second order expansion, excluding a possible tradeoff between the insecurity threshold and the rate of extractable randomness of a protocol. This also contributes to an alternative strong converse proof for QCD due to their exact one-shot correspondence.

A numerical approach for the calculation of QKD key rates allows a uniform framework to be applied to general QKD protocols. Based on our group's previous work, we would like to build a universal software platform that is fully modularized and user-friendly, where one can easily swap in and out different QKD protocol descriptions, channel simulation models or experimental data, backend numerical solvers, and parameter optimization algorithms. Our goal is to build an open-source platform that can be both useful for theorists testing new protocols as well as experimentalists looking for optimal parameters or analyzing their experimental data.